For your first handgun, you want something you are going to be able to shoot a lot. 38spcl or 357 ammo cost 10X more than 22 ammo(assuming you don't reload). With a 22, you'll be able to spend hours at the range for $20. With 357, about 10 minutes.

For that reason, get the 22. You can always pick up 357/38 later. Or a 9mm for that matter, if you desire.